Any maths joke of this type will have obvious holes in it, that's just how maths works

Well the text in the image of the "definition" of a square is clearly tailored to fit this joke, thats why the logic of what a square actually is doesn't apply. Its like telling Diogenes that his chicken is not technically a human because it doesn't have two hands and a nose.

No, it depends on if you have humor. Yes, humor is individual, I know. But people without tend to over analyze and try to pick the joke apart, often missing the point.

A joke doesn't have to pass every technicality. You thinking it's bad if it doesn't, only applies to your humor (or lack there of).